{
  "id": 2909,
  "curve_key": "-1528885655341033442589027839:6002770415671084251911808887221116028159",
  "ainvs": [
    "1",
    "1",
    "1",
    "31851784486271530053938080",
    "-6947650944050483344324943444909373055"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4
  ],
  "naive_height": 187.78300995312026,
  "faltings_height": 13.717608643190722,
  "conductor": "548088118837830139058490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "29",
    "31",
    "37",
    "47",
    "59",
    "61",
    "349",
    "21269"
  ],
  "discriminant": "-2088998983067028655396166839158287669702702441390408514689431935582714215040000",
  "regulator": "1965606.217744365299818339264942494843646289636127023",
  "points": [
    [
      "28681257415193",
      "-156525477377836010207"
    ],
    [
      "12533925382477/9",
      "171002005391306491751/27"
    ],
    [
      "281675077042885",
      "-4728351298329847751755"
    ],
    [
      "116874451549117/9",
      "-1375839280045916825929/27"
    ],
    [
      "5201683925638293307/97969",
      "-11930144300501355145229033239/30664297"
    ],
    [
      "7426292030485",
      "-25281451881701963755"
    ],
    [
      "17058460537101553/7921",
      "-5966702327085518757907283/704969"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2z4old678-067, rational kernel x=-108900008427. Source: https://dujella.github.io/tors/z2z4old678.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.",
  "created_at": "2026-09-26 20:27:56",
  "updated_at": "2026-09-26 20:27:56"
}